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Dynamic Local Strain Measurement From the Digital Image Processing of the Grating Interrogation
V. Vallé, M. Cottron, A. Lagarde
To cite this version:
V. Vallé, M. Cottron, A. Lagarde. Dynamic Local Strain Measurement From the Digital Image
Processing of the Grating Interrogation. Journal de Physique IV Proceedings, EDP Sciences, 1997,
07 (C3), pp.C3-193-C3-198. �10.1051/jp4:1997335�. �jpa-00255492�
J, PIirS IV FRANCE 7 (1 997)
Colloque C3, SupplCment au Journal de Physique I11 d'aofit 1997
Dynamic Local Strain Measurement From the Digital Image Processing of the Grating Interrogation
V.
VallB, M. Cottron and A. LagardeLMS,
SP2MI, Bd 3, Tklkport 2, BP. 179, 86960 Futuroscope cedex, FranceAbstract. The direct measurement of local strains during a dynamic loading is proposed from the spectral analysis of a crossed grating using optical diffraction under oblique incidence This procedure is experimentally achieved with acousto-optic modulators which allow to record 24 strain states at a maximum frequency near to IMHz. The diffraction figures can be recorded on a photographic film or directly on a C.C.D. camera. The automatic localisation of the diffracted spots with the help of data image processing gives the components of the strain tensor. The strain measurement method is performed for compression impact tests using an Hopkinson bar loading.
RCsurni. La mesure directe des diformations en dynamique met i profit l'analyse spectrale de rtseaux croisis par diffraction sous incidence oblique. La mise en oeuvre exptrimentale utilise des modulateurs acousto-optiques qui permettent I'enrcgistrement de 24 ttats de dtformation ?I une frtquence maximum proche du MHz. Les figures de diffraction sont enregistrtes sur plan film ou directement sur camera C.C.D.. La localisation automatique des taches diffracttes au moyen d'une proctdure de traitement et d'analyse d'images fournit les composantes du tenseur des diformations. La mitrologie diveloppie est appliqute sur des essais d'impact en compression par barres d'Hopkinson.
1. INTRODUCTION
Among the experlmental methods, the optical measurement methods occupy an increasing place due to the properties of the l ~ g h t laser source5 and to the easlness of the anallsis using Image processme techniques. The optlcal methods, whlch allow non-contact and non dlsturblng e\aluaa~ons. are well adapted to Investigate dynam~c events. With the use of hlgh speed recording systems. \be c m have access to stresses from photoelastlcity or caustlc method, to d~splacements from hologrsphq or maire interferometry The purpose of our contr~but~on concerns the direct measurement of locd strams dunns a dynamic loadtng from the spectral analys~s of a crossed grating
The gratlng method [ I ] allows to determ~ne the magn~tude and the orientation of h e pmncnpd stram
as well as the rlg~d body rotatlon T h ~ s I S obtained from [2] the comparison betibeen the :come5 of J.
deformed crossed grating (p~tch and orlentation of each direction of grating) \ \ ~ t h L R ~ peonnee of the same grating in the lnlt~al state The analysis of the gratlng is a c h ~ e ~ e d for statlc Inm\csnng.iuonh b? an optical Fourier transform or a numerical one [3] [4] Thls method IS performed for the rnsa~urernem~ of small and large strams In statlc reglme w ~ t h a stram s e n s ~ t ~ v ~ t y [5] comparable to the one obtained h~
strain gauge
Investlgatlons of dynam~c problems from grat~ng analys~s have bccn performed [hj teu dec.ldc~ .ago The complexity of the used procedure has Induced to give up ut~llslng th ~ s technnque The propohzd method, whlch takes advantage of the modern experlmental tool\. I S based on the *prstr-d md!\n\ of .t
crossed gratlng uslng the optical d~ffract~on phenomenon under obl~que 1ncldenc.e The perb~mna.mr'e\ 01 the developed method are demonstrated for the local straln mcasuicrnent method dainmp a d>n.annnnc loading.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1997335
C3-194 JOURNAL
DE
PHYSIQUE IV2. PRINCIPLE
The grating interrogation is performed using optical diffraction of the grating with a variable oblique incidence. By associating with each strain state a specific angle of the incident laser beam, we call separate the diffracted beams during the dynamic event in order to give easier the optical data analysig.
We have so to take account of the diffraction phenomenon in oblique incidence. This phenomenon i \ presented (Figure 1) for an uni-directional grating analysed on reflection by a laser beam.
Figure 1: Oblique diffraction phenomenon
- .
Figure 2: Oblique diffraction of a crossed grating
We give (Figure 2) the diffraction spots issued from a crossed grating. It is necessary to record the 0 order for the determination of the orientation of the measurement base and the diffracted orders + I associated with the two grating families for the measurement of the strain components. The analysih of these 5 diffracted spots is performed by solving [7] a system of 15 equations with 14 unknowns. Thr comparison of these 14 unknowns with the quantities at initial state gives the components of the strain tensor as well as the rigid body motions.
3. RECORDING DEVICE
The variation of the orientation of the incident laser beam and the obtaining of 23 sequential informations during the dynamic event are respectively achieved (Figure 3 and 4) by an acousto-optic deflector and an acousto-optic shutter. The framing rate of this recording device is given by the characteristics of the deflector which allows to record the strain states at a maximum frequency near to 1 MHz. The shutte~.
authorises exposure time equal to 30 ns. The optical element, constituted of a multi facets mirror, permits to move each incident beam towards the optical axis in order to illuminate the same measurement point.
Dynamic loading
Acousto o p t ~ c shJtter
be,iln
Figure 3: Schcrna of thc o p ~ ~ c a l rccc~rding d c \ ~ c c Figure 4: V ~ c u 01 thc opiical rccol-d~ng d c v ~ c c
4. DATA ANALYSIS
we give the repartition of the - 1 , 0 and +I diffraction orders for 23 different orientations of the incident beam. The diffraction figure corresponding to the initial state (Figure 5) is compared to the one (Figure 6) associated with an uniform strain increment.
Figure 5: Initial diffraction figure Figure 6: Deformed diffraction figure
These experimental data can be stored on a photographic film or directly on a C.C.D. camera. Some characteristics of the proposed measurement method depend on the chosen storage way.
4.1 Photographic acquisition
The diffraction figure is recorded on a photographic film . An adapted analysis device has been developed to determine the position of the 115 spots (5 orders of diffraction x 23 states of loading). This device (Figure 7) consists of a XY displacement table for moving the film, and a CCD camera for the acquisition of the spots.
In a first time we create an XY file containing the spots localisation obtained by a global analysis of the film. This analysis is achieved by mounting a photographic lens on the CCD camera and using an appropriate digital image processing. In a second time, we use the XY file to move the film with the motorised displacement table. The diffraction figure is then analysed spot by spot mounting a microscope lens on the CCD camera. By this way, we virtually niultiply [8] the number of pixels of the CCD camera (512x512 pixels to 8000x8000 pixels with 10 prn resolution of the XY displacement) which gives a better localisation of each diffracted spot. This analysis procedure of short duration (about 10 minutes) allows to increase in the same proportion the strain precision of the measurement method.
C3-196 JOUR.NAL
DE
PHYSIQUE IV4.2 C.C.D. camera acquisition
The storage of the diffracted spots is obtained by the synchronisation of the C.C.D. camera acquisitiun with the dynamic loading (Figure 3). The data analysis is then instantaneous using the appropriate digital image processing in order to localise the centre of the spots.
4.3 Characteristics
The strain sensitivity is directly associated to the precision in the determination of the localisation of t h t diffracted spots. We compare (Figure 8 and 9) the strain sensitivity of the method for the two acquisit~on ways. The strain sensitivity obtained from a photographic acquisition reaches 2 . 1 0 ~ when it is (11 approximately 3.10.~ with a C.C.D. camera acquisition. These two quantities are in an equivalent ratio to
the spatial resolution of the C.C.D. sensor used for the analysis (a virtual sensor with 8000x8000 pixel\
for the photographic acquisition, a real sensor with 512x512 pixels for the camera acquisition). T h ~ j confirms that the sensitivity is inversely proportional to the number of pixels of the camera used to analyse the experimental data.
3
(d -5.OE-4-Sensitivity with film acquisition
*
-1.OE-3-5.OE-4
- 1 . 0 ~ - 3
i
--- Sensitivity with CCD acquisition- 1 . 5 E - 3 ! 4 8 3 * ~ 8 8 1 r ~ r 0 3 8 ~ 1 8 8 1 ~
0 5 10 15 20 0 5 10 15 20
step of measurement step of measurement
Figure 8: Strain sensitivity with a film acquisition Figure 9: Strain sensitivity with a CCD acquisition
A study of the optical efficiency of the experimental device shows that the use of a recording film of 400 ASA sensitivity with a 50 mW laser power gives a minimum exposure time equal to 0.5 ps. The direct recording on a C.C.D. camera (512x512 pixels of 8 bits) allows the same experimental conditions.
The maximum strain rate permissible depends on the strain sensitivity and on the exposure time. We give (Table I ) these performances for the two acquisition procedures.
Table 1: Strain rate of the method according to the acquisition procedure
Strain sensitivity Exposure 0.5 p s
time 0.1 p s
Film Camera
2.10.~
400 s"
2000 s-'
3.10.' 6000 s-' 30000 s-'
5. APPLICATIONS
For all the experimental investigations, the diameter of the measurement base is of about 1 mm. The density of the crossed grating is equal to 200 lines per millimetre.
We present (Figure 10) a compression test using the impact of a mass on the mobile grip of the specimen. The storage of the optical data is realised on a photographic film.. We compare the strain optically measured and those obtained by a classical extensometry using a strain gauge. This is achieved by gluing the bi-directional grating on an uniaxial strain gauge. For this test of 600 ps, we have chosen the frame rate equal to 35 kHz and an exposure time of 2.8 ps (10% of frame rate)
We give (Figure 1 I) a compression test performing with a Hopkinson bar loading. The incident bar, the transmission bar and the specimen are in aluminium alloy. The projectile speed is equal to 50 mls. The acquisition of the optical data is directly achieved with a
C.C.D.
camera. The frame rate is equal to 500 kHz with an exposure time equal to 0.2 p s The comparison of the longitudinal strain evolution so determined with those given on the incident bar (gage I) and on the transmission bar (gage 2) shows an identical shape of the evolution with an attenuation of the magnitude during the propagation.Longitudinal s t r a i n (grating) *..* Longitudinal strain (grating)
- . . -
a Transversal s t r a i n (grating) A A A A .Transversal strain (grating) - Longitudinal strain (gage 1)
2.OE-3 Longitudinal s t r a i n (gage) . . . Longitudinal strain (gage 2)
4E-3
-2.OE-3
1
, ,,v,
, , , , , , , , , , , , ,,
Time (s) -3.OE-3
O.OE+O 2.OE-4 4.OE-4 6.OE-4 8.OE-4 1.OE-3
Time (s)
- 8 E - 3 1 I I I I r I
0 20E-6 40E-6 60E-6 80E-6
Figure 10: Strains measurement for 0.6 m s impact duration Figure 11: Strains measurement for 20 ps impact duration
These two dynamic tests give a good idea of the performances of this method. The accordance between longitudinal strains optically determined and classically measured demonstrates the efficiency of the developed method.
6. CONCLUSION
The measurement method performed from an interrogation of a crossed grating using the optical diffraction with an oblique incidence allows to determine the strain tensor as well as the six rigid motions of the measurement base.
The use of acousto-optic components allows to separate easily the information during a dynamic or a static loading and to record 24 states of the specimen at up to 1,000,000 frames per second. The small dimensions of the experimental device and the possibility to employ a classical laser source make an attractive experimental tool of this recording set-up .
The storage of the diffraction figure can be achieved by two ways. One utilises the acquisition on a photographic film analysed by specific device composed by a digital image processing using a CCD camera. The other concerns the direct acquisition on
CCD
camera. The choice of the recording procedure has an influence on some characteristics of the measurement method (strain sensitivity and maximum strain rate). The s c q ~ ~ i r c m e n t of a good strain scnsiti\,ity invol\.e t o s a g e on ;I photographic film. whenC3-198 JOURNAL DE PHYSIQUE IV
the use of the CCD is experimentally easier (the acquisition does not necessitate a total darkness) a11tl
authorises an instantaneous analysis of the optical informations.
The performances of the developed method are demonstrated from dynamic tests. On a measuremeni base of small size, the components of the strain tensor are so optically determined. The accordance w1t11 the strains obtained by classical techniques shows the efficiency of the proposed measurement method.
The direct local determination of strains without any contact consitutes a powerful metrology whiclr can help in the study of many dynamic problems (multiaxial loadings, heterogeneous materials). The extending of the presented optical method for a full field measurement must allow a better understanding of some specific dynamic problems (ductile fracture, adiabatic shear bands).
Acknowledgements
We thank the Search Group GdR "Impact MatCriaux" which has financially supported this study.
References
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B la mesure des grandes et petites dCfonnations", C.R. AcadCmie des Sciences, t. 307, serie I1 (19881 p. 683-688
[3] BrCmand F., DuprC J.C., Lagarde A., "Non-contact and non disturbing local strain measuremenr methods. I - Principle", European Journal of Mechanics, NSolids, vol 11, n03 (1992) p. 349-366 [4] Cardenas-Garcia J.F., Wu M.S., "Further development of the video optical diffractometer for strain
measurement", Proceeding of the SEM Spring Conference (1989)
[5] DuprC J.C., Cottron M., Lagarde A,, 1994, "Grating interrogations: from small to large strain measurement", Experimental Mechnics, vol 35, n02 (1 995) p. 153- 158
[6] Bell J. F.,"Determination of dynamic plastic strain through the use of diffraction gratings", Journal of Applied Physics, Vol27, nOIO (1956) p. 1109-1 113
[7] Valle V., Cottron M., Lagarde A.,"Utilisation du phCnom2ne de diffraction sous incidence obliql~c d'un faisceau laser par un rCseau croisC pour la mesure locale en statique et dynamique des dCformations et des mouvements de solide", Mechanics Research Communications, Vol 22, n02/95 (1995) p. 103-107
[8] Valle V., Cottron M., Lagarde A.,"Dynamic optical method for local strain measurements: principle and characteristics", Proceeding of the Euro Dymat 94, Oxford September, C8, Volume 4 (199-1) p. 59-64
